Let X be a random variable which takes values in the set {1, 2, 3, 4, 5, 6, 7,…
2026
Let X be a random variable which takes values in the set {1, 2, 3, 4, 5, 6, 7, 8}. Further, Pr(X = 1) = Pr(X = 2) = Pr(X = 5) = Pr(X = 7) = 1/6 and Pr(X = 3) = Pr(X = 4) = Pr(X = 6) = Pr(X = 8) = 1/12.
The expected value of X, denoted by E[X], is equal to ___________. (rounded off to two decimal places)
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Correct answer: 4.24 to 4.26
E[X] = Σ x·Pr(X = x). For values 1, 2, 5, and 7, each probability is 1/6, so their contribution is (1 + 2 + 5 + 7)/6 = 15/6 = 2.50. For values 3, 4, 6, and 8, each probability is 1/12, so their contribution is (3 + 4 + 6 + 8)/12 = 21/12 = 1.75. Therefore, E[X] = 2.50 + 1.75 = 4.25. Rounded to two decimal places, the answer is 4.25.